Hydraulic Design of Energy Dissipators for Culverts and Channels Hydraulic Engineering Circular Number 14, Third Edition
Appendix C: Structural Considerations For Roughness Elements
Blocks, sills, and other roughness elements are used to impose exaggerated resistance to flow and to force and stabilize the hydraulic jump. They may be employed inside the culvert barrel, at the culvert exit or in open channels. Roughness elements must be anchored sufficiently to withstand the drag forces on the elements. The fluid dynamic drag equation is:
(C.1)
F_{D} = C_{D} A_{F }ρ V_{a}^{2} /2
where,
C_{D} = coefficient of drag (The maximum C_{D} for a structural angle or a rectangular block is 1.98 (Horner, 1965).)
ρ = density of water, 1000 kg/m^{3} (1.94 slugs/ft^{3})
V_{a} = approach velocity acting on roughness element, m/s (ft/s)
The roughness elements in the CSU rigid boundary basin, the USBR basins, the SAF basin, and internal dissipators must be able to satisfactorily resist the drag force over the lifetime of the structure. The drag force may be assumed to act at the center of the roughness element as shown in Figure C.1.
Figure C.1. Forces Acting on a Roughness Element
The anchor forces necessary to resist overturning can be computed as follows:
(C.2)
F_{A} = hF_{D}/2L_{c} = 0.5 (h/L_{c}) A_{F}ρV_{a}^{2}
where,
F_{A} = total force on anchors
F_{D} = drag force on roughness element
h = height of roughness, m (ft)
L_{C} = distance from downstream edge of roughness element to the centroid of the anchors, m (ft)
A_{F} = frontal area of roughness element, m^{2} (ft^{2})
V_{a} = approach velocity acting on roughness element, m/s (ft/s)
ρ = density of water, 1000 kg/m^{3} (1.94 slugs/ft^{3})
The approach velocity, V_{a}, should be selected as a worst case using the approach velocity at the first row for V_{a}. In cases of tumbling flow or increased resistance on steep slopes, use the normal velocity of the culvert without roughness elements for V_{a}.
